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to edit community portal recent changes upload file special pages search search appearance donate create account log in personal tools donate create account log in contents move to sidebar hide top 1 birth 2 description and works 3 mathematics toggle mathematics subsection 3 1 the diagonal rule bhujā koṭi karṇa nyāya 3 2 cord geometry and the doubling of the square dvikaraṇī 3 3 pi approximation 4 commemoration 5 see also 6 references toggle the table of contents baudhayana 15 languages অসমীয়া বাংলা català deutsch español हिन्दी kreyòl ayisyen italiano मगही മലയാളം پنجابی português संस्कृतम् தமிழ் türkçe edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia redirected from baudhāyana indian sage and mathematician baudhayana बौधायन bas relief in shaheedi park born upvarsha swami bodhayan mandir bangaon village bajpatti block sitamarhi district mithila region bihar monuments swami bodhayan mandir other name bodhayan education tradition taittirīya śākhā kṛṣṇa yajurveda occupations vedic sage sūtrakāra kalpavid era 8th century bce known for baudhayana sutra notable work baudhāyana kalpasūtra śrautasūtra gṛhyasūtra dharmasūtra śulbasūtra parents shankardutt father charumati mother baudhayana sanskrit बौधायन romanised baudhāyana believed to have lived around the 8th century bce was a vedic scholar and sūtrakāra affiliated with the taittirīya śākhā of the kṛṣṇa yajurveda 1 he is known for having written the baudhāyana kalpasūtra a foundational manual of the kalpa vedānga which contains the baudhāyana śulbasūtra the oldest known work on geometry and ritual mathematics 2 his birth anniversary is known as baudhāyana jayanti or bodhayan jayanti or bodhayan janmotsav in the mithila region 3 birth edit in local traditions of the mithila region baudhāyana is also called as bhagwan bodhayana according to these accounts he was born on the dwadashi twelfth day in krishna paksha waning phase in the hindu calendar month of pausha he is believed to have born in bangaon village located in the bajpatti block of sitamarhi district bihar his childhood name was upvarsha 4 5 his was the son of shankardutt a scholar of pataliputra 6 and charumati description and works edit baudhāyana is traditionally regarded as one of the earliest sūtrakāras systematizers affiliated with the taittirīya śākhā school of the kṛṣṇa yajurveda 1 his corpus forms the baudhāyana kalpasūtra a comprehensive manual belonging to the kalpa vedāṅga one of the six auxiliary disciplines essential for proper study and the practice of vedic texts 2 the baudhāyana kalpasūtra is a multi part canonical work comprising 7 śrautasūtra procedures for public vedic sacrifices yajñas gṛhyasūtra domestic rites and household sacraments saṃskāras dharmasūtra ethical legal and social codes śulbasūtra geometric principles spatial layouts and construction rules for fire altars vedis and citis pariśiṣṭas karmāntasūtras supplementary procedural manuals in the vedic classification of knowledge vidyā applied science such as śulba śāstra geometry and jyotiṣa astronomy and calendar calculation were practiced as aparā vidyā these are essential empirical disciplines developed to sustain the cosmic and ritual harmony required by the vedic tradition 2 dating from approximately the eighth century bce baudhāyana was one of the earliest theorists who formulated the geometric principles such that it directly addressed spatial and numerical calculations in ancient india 1 later folklore and regional traditions sometimes identify baudhāyana with the commentator upavarṣa 7 the baudhāyana śākhā school preserved traditions of ritual practice and theology within the taittirīya tradition this included early references to veneration of vishnu as mahāpuruṣa alongside other vedic deities 8 9 the dates of the major śulbasūtras baudhāyana mānava and āpastambha are estimated between the 8th and 5th centuries bce with baudhyāna sūtras generally placed earliest around 800 bce 10 1 mathematics edit the baudhāyana śulbasūtra derived from the sanskrit root śulb meaning to measure or cord constitutes the earliest written manual of indian geometry 11 the śulba tradition was closely associated with the practical requirements of vedic ritual particularly the measurement and construction of fire altars and expressed geometrical knowledge through procedures of measurement and construction 2 vedic altars were required to adhere to precise geometric shapes specific altar types such as the falcon shaped śyenaciti circular gārhapatya square āhavanīya and semicircular dakṣiṇāgni were mandated to have identical surface areas or scaled proportions 12 these requirements necessitated exact geometric solutions for area preserving transformations constructing a square equal in area to a circle and vice versa the diagonal rule bhujā koṭi karṇa nyāya formulating the relation between the base bhujā altitude koṭi and diagonal karṇa of rectangles and squares surd approximations calculating accurate square roots such as 2 displaystyle sqrt 2 up to five decimal places using recursive fractional steps for cord alignment in the sūtra tradition geometric validations were demonstrated through practical construction upapatti or visual demonstration or oral transmission as opposed to written proofs 11 13 the diagonal rule bhujā koṭi karṇa nyāya edit in the baudhāyana śulbasūtra the geometric relationship governing right angled triangles and rectangles is expressed as the cord rule nyāya relating the horizontal base bhujā vertical altitude koṭi and diagonal karṇa 14 prior to the general theorem for rectangles bs 1 9 establishes the special case for the square समचतुरश्रस्याक्ष्णया रज्जुर्द्विस्तावतीं भूमिं करोति samacaturaśrasyākṣṇayā rajjudvistāvatīṃ bhūmiṃ karoti baudhāyana śulbasūtra 1 9 meaning the diagonal of a square produces double the area of that square 15 in bs 1 12 baudhāyana states the general theorem for any rectangle दीर्घचतुरश्रस्याक्ष्णया रज्जुः पार्श्वमानी तिर्यङ् मानी च यत् पृथग् भूते कुरुतस्तदुभयं करोति dīrghacaturaśrasyākṣṇayā rajjuḥ pārśvamānī tiryaṅmānī ca yat pṛthagbhūte kurutastadubhayaṃ karoti baudhāyana śulbasūtra 1 12 meaning the areas of the squares produced separately by the length and the breadth of a rectangle together equal the area of the square produced by the diagonal 15 this is followed in bs 1 13 by a catalogue of integer rectangle sides that satisfy this rule defining what are known in modern mathematics as pythagorean triples 3 4 5 5 12 13 8 15 17 7 24 25 and 12 35 37 11 according to mathematician s g dani the babylonian cuneiform tablet plimpton 322 written c 1850 bce 16 contains fifteen pythagorean triples with quite large entries including 13500 12709 18541 which is a primitive triple 17 indicating in particular that there was sophisticated understanding on the topic in mesopotamia in 1850 bce since these tablets predate the sulbasutras period by several centuries taking into account the contextual appearance of some of the triples it is reasonable to expect that similar understanding would have been there in india 18 cord geometry and the doubling of the square dvikaraṇī edit to construct a sacrificial altar with twice the surface area of a given square altar baudhāyana formulated the rule of dvikaraṇī the multiplier of the diagonal or 2 displaystyle sqrt 2 in bs 1 61 62 this value is given as a sequence of fractional additions 19 2 1 1 3 1 3 4 1 3 4 34 577 408 1 4142156 displaystyle sqrt 2 approx 1 frac 1 3 frac 1 3 times 4 frac 1 3 times 4 times 34 frac 577 408 approx 1 4142156 the expression is accurate up to five decimal places 20 21 this expression is similar in structure to the expression found on a mesopotamian tablet 22 from the old babylonian period 1900 1600 bce 2 23 the text contains geometric solutions of linear and quadratic equations although these are expressed through geometric constructions rather than in explicit algebraic forms such as a x 2 c displaystyle ax 2 c and a x 2 b x c displaystyle ax 2 bx c these techniques allowed ritual architects to transform rectangular altars into squares and circular hearths into squares without altering the total surface area 24 25 26 pi approximation edit shulba sutras gave approximations of pi value which can be interpreted as approximately 3 08831 3 08833 3 004 3 or 3 125 27 25 commemoration edit since 1957 an annual commemoration known as baudhāyana jayanti or bodhayan janmotsav has been observed at the swami bodhayan mandir in the sitamarhi district of bihar 28 29 30 the annual observance includes community processions kalash yatra recitation and temple rituals in 2022 proposals were put forward to the department of art and culture of bihar to recognize the annual commemoration as an official regional festival 31 32 4 33 see also edit pythagoras theorem plimpton 322 references edit 1 2 3 4 sen s n bag a k 1983 the śulba sūtras of baudhāyana āpastamba kātyāyana and mānava new delhi indian national science academy pp 1 15 1 2 3 4 5 datta bibhutibhusan 1932 the science of the sulba a study in early hindu geometry university of calcutta pp 1 7 divakaran p p september 19 2018 the mathematics of india springer nature singapore p 46 isbn 9789811317743 1 2 भगवान बोधायन की तपस्थली बोधायनसर को अब मिल सकेगी विश्वव्यापी ख्याति bodhanyansar the ascetic place of lord bodhayan will now be able to gain worldwide fame bihar sitamarhi general news jagran in hindi retrieved 2025 07 13 गणितज्ञ बोधायन की जयंती आज पर्यटन केंद्र के रूप में होगा विकसित jagran in hindi retrieved 2025 07 12 तैयारियां पूरी दार्शनिक गणितज्ञ भगवान बोधायन की जयंती आज dainik bhaskar in hindi 2019 01 02 archived from the original on 2021 08 03 retrieved 2025 07 12 1 2 olivelle patrick 1999 dharmasūtras the law codes of āpastamba gautama baudhāyana and vasiṣṭha oxford university press pp xxv xxviii isbn 978 0192838827 davis richard h 2024 religions of early india a cultural history princeton university press isbn 978 0691199269 davis richard h 2024 11 26 religions of early india a cultural history princeton university press isbn 978 0 691 19926 9 sulba sutras indian mathematics pdf rutgers university retrieved 2026 06 07 1 2 3 joseph george gheverghese 2010 the crest of the peacock non european roots of mathematics 3rd ed princeton university press pp 306 322 isbn 978 0691135267 seidenberg a 1962 the ritual origin of geometry archive for history of exact sciences 1 5 488 527 doi 10 1007 bf00327767 plofker kim 2009 mathematics in india princeton university press pp 17 18 isbn 978 0 691 12067 6 divakaran p p 2018 the mathematics of india concepts methods connections springer nature pp 46 47 isbn 978 9811317743 1 2 thibaut george 1875 on the śulvasútras journal of the asiatic society of bengal 44 227 275 mathematics department university of british columbia the babylonian tabled plimpton 322 archived 17 june 2020 at the wayback machine three positive integers a b c displaystyle a b c form a primitive pythagorean triple if c 2 a 2 b 2 and if the highest common factor of a b c is 1 in the particular plimpton322 example this means that 13500 2 12709 2 18541 2 and that the three numbers do not have any common factors however some scholars have disputed the pythagorean interpretation of this tablet see plimpton 322 for details dani 2003 harv error no target citerefdani2003 help gupta r c 1972 baudhāyana s value of 2 the mathematics education 6 3 b77 b79 the value of this approximation 577 408 is the seventh in a sequence of increasingly accurate approximations 3 2 7 5 17 12 to 2 the numerators and denominators of which were known as side and diameter numbers to the ancient greeks and in modern mathematics are called the pell numbers if x y is one term in this sequence of approximations the next is x 2 y x y these approximations may also be derived by truncating the continued fraction representation of 2 henderson david w 2000 square roots in the śulba sūtras in gorini catherine a ed geometry at work papers in applied geometry mathematical association of america notes vol 53 washington d c the mathematical association of america pp 39 45 isbn 978 0883851647 neugebauer o and a sachs 1945 mathematical cuneiform texts new haven ct yale university press p 45 cooke roger 1997 the history of mathematics a brief course internet archive new york wiley isbn 978 0 471 18082 1 cite book cs1 maint publisher location link sen s n bag a k 1983 the śulba sūtras of baudhāyana āpastamba kātyāyana and mānava new delhi indian national science academy pp 15 28 1 2 o connor john j robertson edmund f baudhayana mactutor history of mathematics archive university of st andrews retrieved 9 june 2026 kim plofker 2009 mathematics in india princeton university press pp 17 18 isbn 978 0 691 12067 6 plofker kim 2009 mathematics in india princeton university press p 27 isbn 978 0 691 12067 6 बिहार के ऐसे गणितज्ञ जिनकी थ्योरम प्रयोग कर आर्यभट्ठ ने की थी अंतरिक्ष की कई खोज पाणिनि के थे गुरु news18 हिंदी in hindi 2024 12 20 retrieved 2025 07 13 भगवान बोधायन की जयंती आज in hindi 2024 12 27 archived from the original on 2025 04 18 retrieved 2025 07 13 भगवान बोधायन की तपस्थली बोधायनसर को अब मिल सकेगी विश्वव्यापी ख्याति bodhanyansar the ascetic place of lord bodhayan will now be able to gain worldwide fame dainik jagran in hindi 13 july 2023 retrieved 13 july 2025 बोधायन गणितज्ञ ही नहीं बल्कि ज्योतिषाचार्य व वेदज्ञ थे मंत्री baudhayana was not only a mathematician but also an astrologer and vedic scholar minister hindustan in hindi 28 december 2022 शोभायात्रा बोधायन जयंती 20 को 14 को कलश शोभायात्रा dainik bhaskar बोधायन गणितज्ञ ही नहीं बल्कि ज्योतिषाचार्य व वेदज्ञ थे मंत्री hindustan 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